The extended collaborative representation-based classification

Collaborative representation (CR), one of the well-known representation methods, has been widely used in pattern recognition. The collaborative representation-based classification (CRC) is to represent a test sample by the collaborative subspace of all the training samples from all classes. As an effective extension of CRC, the probabilistic collaborative representation-based classification (PCRC) calculates the probability of a test sample belonging to the collaborative subspace of all classes for classification. In the related CRC works, the representation fidelity is often measured by the ℓ
₂
-norm of coding residual, but the ℓ
₁
-norm fidelity is used very little. In fact, the representation fidelity with different coding residuals has a great effect on the CR-based classification performance. In this paper, to further improve the CR-based classification accuracy, we propose the extended CRC and PCRC by jointing the ℓ
₁
-norm and ℓ
₂
-norm of coding residuals on the representation fidelity. Besides, the extension of CRC is introduced by constraining the coding residual with ℓ
₁
-norm. The experiments on four popular face databases show that the proposed extensions of CRC and PCRC perform very well.